Let us now analyze the case in which \(f^{-1}[a,b]\cap \textnormal {Crit}(f)\ne \emptyset \) . The main reference for the basic ideas we will be following in this case may be for instance [1]}. Let \(y\xleftarrow{}x\)  be a non-degenerate critical arrow. We will denote by \(\xi _0:\nu (\mathcal {O}_x)\rightarrow \nu _-(\mathcal {O}_x)\)  and \(\eta _0:\nu (\mathcal {O}_x)\rightarrow \nu _+(\mathcal {O}_x)\)  the two mutually complementary projections. They induce bundle morphisms between the bundle projections \(\pi :\nu (\mathcal {O}_x)\rightarrow \mathcal {O}_x\)  and \(\pi _{\pm }:\nu _\pm (\mathcal {O}_x)\rightarrow \mathcal {O}_x\) , respectively. Moreover, for every \(v\in \nu (\mathcal {O}_x)\)  we have that \(v=\xi _0(v)+\eta _0(v)\)  and the expression
\(\Vert  v\Vert _0^2=-Q_f(\xi _0(v))+Q_f(\eta _0(v)),\) 
